THE HUBBLE LAW

Please print out these instructions to refer to them while you are using the applet.

Here you will have an opportunity to measure redshifts for several galaxies using a set of common spectral lines here. While the spectra that you will be using have many lines (emission and absorption) concentrate on using the following sets:

Calcium H and K

These are very prominent absorption lines is most all galaxies. An example is shown here:

These pair of absorption lines will appear in all the spectra and they should be your principle source for determining the redshift. The rest wavelengths of these lines are 3933 angstroms and 3968 angstrons.

A radial velocity of a galaxy is determined from the redshift as follows:

Vr = cz

where c = speed of light = 300,000 km/s

and z = redshift

To determine the redshift z, you need to calculate from the spectra the ratio of the observed wavelengths of the H and K lines to their rest wavelengths.

For example, suppose the observed wavelengths of these two lines are 3953 and 3988 angstroms.

In this case the redshift z = (3953-3933)/3933 or 0.005.

or

z = (3988 - 3968)/3968 = 0.005.

The velocity of the galaxy would then be 300,000 x .005 = 1500 km/s.

Hydrogen Emission Lines

In addition, some galaxies have emission lines that are principally due to hydrogren recombination. One of these lines that appears in these spectra is H-beta which is shown below:

Note that not all the galaxies have this line but in those cases where its present, it should be measured in addition to the Calcium H and K lines. The wave length of this line is 4861 Angstroms.

When this applet opens you will see an iconic representation of galaxies in the left hand side of the applet and a target area in the right side of the applet. If you click on a galaxy its name will appear and an image of that galaxy will be located in the target. You can grab the image of the galaxy with the pointer (mouse) and center it in the target. This is how you will measure the angular diameter of the galaxy. Simply count or estimate the number of red rings that it takes to fully enclose the galaxy image and use that number as your measurment of diameter (note: for experts, the rings have a constant offset in units of arcseconds).

You should now write down the galaxy name and its diameter.

Next click on the tab marked spectrum. The actual spectrum of this galaxy will then be loaded. The green line can be dragged around and the wavelength will be shown. You need to identify the Ca II H and K lines in the spectra (these may now always be easy) and measure them. By measuring we mean dragging the green line to the approximate center of the feature and then clicking on the button labeled record measurement.

You should measure both lines this way and also the H-beta emission line if it is present.

In the image below, an example spectra is shown with these features marked. This is what you need to look for in the spectra that you will examine.

After doing this now go to the tab marked data where you will see the wavelengths of the lines that you just measured. Write down those wavelengths along with the galaxy name and diameter.

Do this procedure for 10 randomly selected galaxies (about 30 are available) and answer the following questions (at the very bottom of this page is the link to actual applet)

Exercises:

1. Calculate the redshift for each of the galaxies from your measurements in combination with the rest frame wavelengths given above.

2. Determine from your data if there is a relation (you can graph the data if you like) between the angular size that you measured and the size of the redshift.

3. If indeed there is a relation, what assumption would you have to make to use this data to show that the Universe is expanding. Note: What you are doing in this excercise is identical to what Hubble did in the 1920's and you are using the same galaxies.

Now go to the applet